• Corpus ID: 219646073

AN AUGMENTED IIM FOR HELMHOLTZ/POISSON EQUATIONS ON IRREGULAR DOMAINS IN COMPLEX SPACE

@inproceedings{Zhang2015ANAI,
  title={AN AUGMENTED IIM FOR HELMHOLTZ/POISSON EQUATIONS ON IRREGULAR DOMAINS IN COMPLEX SPACE},
  author={Sidong Zhang and Liu Zhilin},
  year={2015}
}
In this paper, an augmented immersed interface method has been developed for Helmholtz/Poisson equations on irregular domains in complex space. One of motivations of this paper is for simulations of wave scattering in different geometries. This paper is the first immersed interface method in complex space. The new method utilizes a combination of methodologies including the immersed interface method, a fast Fourier transform, augmented strategies, least squares interpolations, and the… 

Figures and Tables from this paper

Solving Interface Problems of the Helmholtz Equation by Immersed Finite Element Methods

This article reports the explorations for solving interface problems of the Helmholtz equation by immersed finite elements (IFE) on interface independent meshes with partially penalized and discontinuous Galerkin IFE methods.

A fast high-order algorithm for the multiple cavity scattering

A fast high-order algorithm is proposed for solving the electromagnetic scattering from multiple cavities embedded in an infinite ground plane by means of a transparent boundary condition that results in a big system involving the Helmholtz equations with the coupled transparent boundary conditions, which is further reduced to a small system that includes only the coupling of the aperture system of each cavity.

Immersed Finite Elements for a Second Order Elliptic Operator and Their Applications

References

SHOWING 1-10 OF 14 REFERENCES

An immersed finite element space and its approximation capability

This article discusses an immersed finite element (IFE) space introduced for solving a second‐order elliptic boundary value problem with discontinuous coefficients (interface problem). The IFE space

The immersed boundary method

This paper is concerned with the mathematical structure of the immersed boundary (IB) method, which is intended for the computer simulation of fluid–structure interaction, especially in biological

A Fast Iterative Algorithm for Elliptic Interface Problems

The idea in this approach is to precondition the differential equation before applying the immersed interface method, and to take advantage of fast Poisson solvers on a rectangular region, an intermediate unknown function, the jump in the normal derivative across the interface, is introduced.

the immersed interface method for elliptic equations with discontinuous coefficients and singular sources

The authors develop finite difference methods for elliptic equations of the form \[ \nabla \cdot (\beta (x)\nabla u(x)) + \kappa (x)u(x) = f(x)\] in a region $\Omega $ in one or two space dimension...

A Numerical Study of Electro-migration Voiding by Evolving Level Set Functions on a Fixed Cartesian Grid

A numerical method for studying migration of voids driven by surface diffusion and electric current in a metal conducting line is developed. The mathematical model involves moving boundaries governed

Numerical analysis of blood flow in the heart

An algorithm for the machine calculation of complex Fourier series

Good generalized these methods and gave elegant algorithms for which one class of applications is the calculation of Fourier series, applicable to certain problems in which one must multiply an N-vector by an N X N matrix which can be factored into m sparse matrices.

Interface problems and methods in biological and physical flows

An Introduction to the Immersed Boundary and the Immersed Interface Methods Lecture Notes on Nonlinear Tumor Growth: Modeling and Simulation Progress in Modeling Pulsed Detonations Direct Numerical

GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems

We present an iterative method for solving linear systems, which has the property of minimizing at every step the norm of the residual vector over a Krylov subspace. The algorithm is derived from t...

Applied Numerical Linear Algebra

The symmetric Eigenproblem and singular value decomposition and the Iterative methods for linear systems Bibliography Index.